Causal tracing systematically intervenes on a large language model's (LLM's) internal representations to uncover and quantify the causal pathways linking specific inputs or computations to specific metrics of interest, quantifying the LLM's behavior.Building on previous single-component or single-layer studies, this paper presents a unified framework for causally tracing multiple components simultaneously.This framework systematically identifies the subsets of components (e.g., attention heads and multi-layer perceptron neurons) most critical to a desired target performance metric (e.g., accuracy and fairness).This is achieved by incorporating flexible interventions applied to a wide range of desired metrics.To address the combinatorial complexity of the multicomponent problem, an efficient algorithm is designed that leverages soft interventions and a carefully designed metric transformation, converting the combinatorial search problem into a continuous one that can be solved efficiently under proper constraints, thereby generating proper binary decisions for selecting components.Experimental results demonstrate that the proposed method efficiently identifies subsets of the model's components that have a high impact on the target metric, outperforming existing baseline approaches.Our code is available at https://github.com/ZiruiYan/ multi-component-causal-tracing.

This paper considers causal bandits (CBs) for the sequential design of interventions in a causal system. The objective is to optimize a reward function via minimizing a measure of cumulative regret with respect to the best sequence of interventions in hindsight. The paper advances the results on CBs in three directions. First, the structural causal models (SCMs) are assumed to be unknown and drawn arbitrarily from a general class $\mathcal{F}$ of Lipschitz-continuous functions. Existing results are often focused on (generalized) linear SCMs. Second, the interventions are assumed to be generalized soft with any desired level of granularity, resulting in an infinite number of possible interventions. The existing literature, in contrast, generally adopts atomic and hard interventions. Third, we provide general upper and lower bounds on regret. The upper bounds subsume (and improve) known bounds for special cases. The lower bounds are generally hitherto unknown. These bounds are characterized as functions of the (i) graph parameters, (ii) eluder dimension of the space of SCMs, denoted by $\mathrm{dim}(\mathcal{F})$, and (iii) the covering number of the function space, denoted by $\mathrm{cn}(\mathcal{F})$. Specifically, the cumulative achievable regret over horizon $T$ is $\mathcal{O}(K d^{L-1}\sqrt{T\,\mathrm{dim}(\mathcal{F}) \log(\mathrm{cn}(\mathcal{F}))})$, where $K$ is related to the Lipschitz constants, $d$ is the graph’s maximum in-degree, and $L$ is the length of the longest causal path. The upper bound is further refined for special classes of SCMs (neural network, polynomial, and linear), and their corresponding lower bounds are provided.

Causal interactions among a group of variables are often modeled by a single causal graph. In some domains, however, these interactions are best described by multiple co-existing causal graphs, e.g., in dynamical systems or genomics. This paper addresses the hitherto unknown role of interventions in learning causal interactions among variables governed by a mixture of causal systems, each modeled by one directed acyclic graph (DAG). Causal discovery from mixtures is fundamentally more challenging than single-DAG causal discovery. Two major difficulties stem from (i) an inherent uncertainty about the skeletons of the component DAGs that constitute the mixture and (ii) possibly cyclic relationships across these component DAGs. This paper addresses these challenges and aims to identify edges that exist in at least one component DAG of the mixture, referred to as the *true* edges. First, it establishes matching necessary and sufficient conditions on the size of interventions required to identify the true edges. Next, guided by the necessity results, an adaptive algorithm is designed that learns all true edges using ${\cal O}(n^2)$ interventions, where $n$ is the number of nodes. Remarkably, the size of the interventions is optimal if the underlying mixture model does not contain cycles across its components. More generally, the gap between the intervention size used by the algorithm and the optimal size is quantified. It is shown to be bounded by the *cyclic complexity number* of the mixture model, defined as the size of the minimal intervention that can break the cycles in the mixture, which is upper bounded by the number of cycles among the ancestors of a node.

Given a set of discrete probability distributions, the minimum entropy coupling is the minimum entropy joint distribution that has the input distributions as its marginals. This has immediate relevance to tasks such as entropic causal inference for causal graph discovery and bounding mutual information between variables that we observe separately. Since finding the minimum entropy coupling is NP-Hard, various works have studied approximation algorithms. The work of [Compton, 2022] shows that the greedy coupling algorithm of [Kocaoglu et al., 2017a] is always within $\log_2(e)$ $\approx$ 1.44 bits of the optimal coupling. Moreover, they show that it is impossible to obtain a better approximation guarantee using the majorization lower-bound that all prior works have used: thus establishing a majorization barrier. In this work, we break the majorization barrier by designing a stronger lower-bound that we call the profile method. Using this profile method, we are able to show that the greedy algorithm is always within $\log_2(e)/e$ $\approx$ 0.53 bits of optimal for coupling two distributions (previous best-known bound is within 1 bit), and within $(1 + \log_2(e))/2$ $\approx$ 1.22 bits for coupling any number of distributions (previous best-known bound is within 1.44 bits). We also examine a generalization of the minimum entropy coupling problem: Concave Minimum-Cost Couplings. We are able to obtain similar guarantees for this generalization in terms of the concave cost function. Additionally, we make progress on the open problem of [Kovačević et al., 2015] regarding NP membership of the minimum entropy coupling problem by showing that any hardness of minimum entropy coupling beyond NP comes from the difficulty of computing arithmetic in the complexity class NP. Finally, we present exponential-time algorithms for computing the exactly optimal solution. We experimentally observe that our new profile method lower bound is not only helpful for analyzing the greedy approximation algorithm, but also for improving the speed of our new backtracking-based exact algorithm.

Entropic causal inference is a recent framework for learning the causal graph between two variables from observational data by finding the information-theoretically simplest structural explanation of the data, i.e., the model with smallest entropy. In our work, we first extend the causal graph identifiability result in the two-variable setting under relaxed assumptions. We then show the first identifiability result using the entropic approach for learning causal graphs with more than two nodes. Our approach utilizes the property that ancestrality between a source node and its descendants can be determined using the bivariate entropic tests. We provide a sound sequential peeling algorithm for general graphs that relies on this property. We also propose a heuristic algorithm for small graphs that shows strong empirical performance. We rigorously evaluate the performance of our algorithms on synthetic data generated from a variety of models, observing improvement over prior work. Finally we test our algorithms on real-world datasets.

Thousands of scientific publications discuss evidence on the efficacy of non-cancer generic drugs being tested for cancer. However, trying to manually identify and extract such evidence is intractable at scale. We introduce a natural language processing pipeline to automate the identification of relevant studies and facilitate the extraction of therapeutic associations between generic drugs and cancers from PubMed abstracts. We annotate datasets of drug-cancer evidence and use them to train models to identify and characterize such evidence at scale. To make this evidence readily consumable, we incorporate the results of the models in a web application that allows users to browse documents and their extracted evidence. Users can provide feedback on the quality of the evidence extracted by our models. This feedback is used to improve our datasets and the corresponding models in a continuous integration system. We describe the natural language processing pipeline in our application and the steps required to deploy services based on the machine learning models.

The estimation of causal treatment effects from observational data is a fundamental problem in causal inference. To avoid bias, the effect estimator must control for all confounders. Hence practitioners often collect data for as many covariates as possible to raise the chances of including the relevant confounders. While this addresses the bias, this has the side effect of significantly increasing the number of data samples required to accurately estimate the effect due to the increased dimensionality. In this work, we consider the setting where out of a large number of covariates $X$ that satisfy strong ignorability, an unknown sparse subset $S$ is sufficient to include to achieve zero bias, i.e. $c$-equivalent to $X$. We propose a common objective function involving outcomes across treatment cohorts with nonconvex joint sparsity regularization that is guaranteed to recover $S$ with high probability under a linear outcome model for $Y$ and subgaussian covariates for each of the treatment cohort. This improves the effect estimation sample complexity so that it scales with the cardinality of the sparse subset $S$ and $\log |X|$, as opposed to the cardinality of the full set $X$. We validate our approach with experiments on treatment effect estimation.

More than 200 generic drugs approved by the U.S. Food and Drug Administration for non-cancer indications have shown promise for treating cancer. Due to their long history of safe patient use, low cost, and widespread availability, repurposing of these drugs represents a major opportunity to rapidly improve outcomes for cancer patients and reduce healthcare costs. In many cases, there is already evidence of efficacy for cancer, but trying to manually extract such evidence from the scientific literature is intractable. In this emerging applications paper, we introduce a system to automate non-cancer generic drug evidence extraction from PubMed abstracts. Our primary contribution is to define the natural language processing pipeline required to obtain such evidence, comprising the following modules: querying, filtering, cancer type entity extraction, therapeutic association classification, and study type classification. Using the subject matter expertise on our team, we create our own datasets for these specialized domain-specific tasks. We obtain promising performance in each of the modules by utilizing modern language processing techniques and plan to treat them as baseline approaches for future improvement of individual components.

Entropic causal inference is a framework for inferring the causal direction between two categorical variables from observational data. The central assumption is that the amount of unobserved randomness in the system is not too large. This unobserved randomness is measured by the entropy of the exogenous variable in the underlying structural causal model, which governs the causal relation between the observed variables. Kocaoglu et al. conjectured that the causal direction is identifiable when the entropy of the exogenous variable is not too large. In this paper, we prove a variant of their conjecture. Namely, we show that for almost all causal models where the exogenous variable has entropy that does not scale with the number of states of the observed variables, the causal direction is identifiable from observational data. We also consider the minimum entropy coupling-based algorithmic approach presented by Kocaoglu et al., and for the first time demonstrate algorithmic identifiability guarantees using a finite number of samples. We conduct extensive experiments to evaluate the robustness of the method to relaxing some of the assumptions in our theory and demonstrate that both the constant-entropy exogenous variable and the no latent confounder assumptions can be relaxed in practice. We also empirically characterize the number of observational samples needed for causal identification. Finally, we apply the algorithm on Tuebingen cause-effect pairs dataset.

A growing body of work has begun to study intervention design for efficient structure learning of causal directed acyclic graphs (DAGs). A typical setting is a \emph{causally sufficient} setting, i.e. a system with no latent confounders, selection bias, or feedback, when the essential graph of the observational equivalence class (EC) is given as an input and interventions are assumed to be noiseless. Most existing works focus on \textit{worst-case} or \textit{average-case} lower bounds for the number of interventions required to orient a DAG. These worst-case lower bounds only establish that the largest clique in the essential graph \textit{could} make it difficult to learn the true DAG. In this work, we develop a \textit{universal} lower bound for single-node interventions that establishes that the largest clique is \textit{always} a fundamental impediment to structure learning. Specifically, we present a decomposition of a DAG into independently orientable components through \emph{directed clique trees} and use it to prove that the number of single-node interventions necessary to orient any DAG in an EC is at least the sum of half the size of the largest cliques in each chain component of the essential graph. Moreover, we present a two-phase intervention design algorithm that, under certain conditions on the chordal skeleton, matches the optimal number of interventions up to a multiplicative logarithmic factor in the number of maximal cliques. We show via synthetic experiments that our algorithm can scale to much larger graphs than most of the related work and achieves better worst-case performance than other scalable approaches. A code base to recreate these results can be found at \url{https://github.com/csquires/dct-policy}.

Directed acyclic graph (DAG) models are popular for capturing causal relationships. From observational and interventional data, a DAG model can only be determined up to its \emph{interventional Markov equivalence class} (I-MEC). We investigate the size of MECs for random DAG models generated by uniformly sampling and ordering an Erdős-Rényi graph. For constant density, we show that the expected $\log$ observational MEC size asymptotically (in the number of vertices) approaches a constant. We characterize I-MEC size in a similar fashion in the above settings with high precision. We show that the asymptotic expected number of interventions required to fully identify a DAG is a constant. These results are obtained by exploiting Meek rules and coupling arguments to provide sharp upper and lower bounds on the asymptotic quantities, which are then calculated numerically up to high precision. Our results have important consequences for experimental design of interventions and the development of algorithms for causal inference.

We consider the problem of experimental design for learning causal graphs that have a tree structure. We propose an adaptive framework that determines the next intervention based on a Bayesian prior updated with the outcomes of previous experiments, focusing on the setting where observational data is cheap (assumed infinite) and interventional data is expensive. While information greedy approaches are popular in active learning, we show that in this setting they can be exponentially suboptimal (in the number of interventions required), and instead propose an algorithm that exploits graph structure in the form of a centrality measure. If infinite interventional data is available, we show that the algorithm requires a number of interventions less than or equal to a factor of 2 times the minimum achievable number. We show that the algorithm and the associated theory can be adapted to the setting where each performed intervention yields finitely many samples. Several extensions are also presented, to the case where a specified set of nodes cannot be intervened on, to the case where $K$ interventions are scheduled at once, and to the fully adaptive case where each experiment yields only one sample. In the case of finite interventional data, through simulated experiments we show that our algorithms outperform different adaptive baseline algorithms.

Predictive modeling is becoming increasingly common in healthcare. Existing healthcare cost prediction solutions are tailor-made to accomplish specific tasks for certain populations, hence requiring expensive modifications to adapt to a different task or population. In this paper, we present a modular and extensible solution for healthcare cost prediction, which can be easily configured for various prediction tasks and populations. Our solution incorporates efficient high-dimensional data handling, smart feature engineering, flexible predictive learning, individualized assessment of cost impacts of predictors, and a management system that allows for reuse of partial results. We configure two distinct applications using the proposed system and present results on prediction accuracy and cost impact assessment. The first application predicts healthcare costs for a commercial population, and the second predicts the cost of care for a Medicaid population using an entirely different set of data, predictors, and assumptions.

Motivated by the cloud computing paradigm, and by key optimization problems in all-optical networks, we study two variants of the classic job interval scheduling problem, where a reusable resource is allocated to competing job intervals in a flexible manner. Each job, Ji, requires the use of up to rmax(i) units of the resource, with a profit of pi ≥ 1 accrued for each allocated unit. The goal is to feasibly schedule a subset of the jobs so as to maximize the total profit. The resource can be allocated either in contiguous or non-contiguous blocks. These problems can be viewed as flexible variants of the well known storage allocation and bandwidth allocation problems.

We develop a new local search algorithm for binary optimization problems, whose complexity and performance are explicitly controlled by a parameter Q, measuring the depth of the local search neighborhood. We show that the algorithm is pseudo-polynomial for general cost vector c, and achieves a w 2 /(2w-1) approximation guarantee for set packing problems with exactly w ones in each column of the constraint matrix A, when using Q = w 2 . Most importantly, we find that the method has practical promise on large, randomly generated instances of both set covering and set packing problems, as it delivers performance that is competitive with leading general-purpose optimization software (CPLEX 11.2).

Signals in response to time-localized events of a common phenomenon tend to exhibit a common shape, but with variable time scale, amplitude, and delay across trials in many domains. We develop a new formulation to learn the common shape and variables from noisy signal samples with a Bayesian signal model and a Markov chain Monte Carlo inference scheme involving Gibbs sampling and independent Metropolis-Hastings. Our experiments with generated and real-world data show that the algorithm is robust to missing data, outperforms the existing approaches and produces easily interpretable outputs.

One of the key computational problems in combinatorics/statistical physics is the problem of computing limits of the log-partition functions for various statistical mechanics models on lattices. In combinatorics this limit corresponds to the exponent of various arrangements on lattices, for example the exponents of the number of independent sets, proper colorings or matchings on a lattice. In statistical physics this limit is called free energy. We propose a new method, sequential cavity, which beats the best known existing methods, such as transfer matrix method, in obtaining sharper bounds on the limits of the log-partition function for two models: independent sets (hard-core) and matchings (monomer-dimer). Our method is based on a surprisingly simple representation of the log-partition function limit in terms of a certain marginal probability of a suitably modified lattice, and using recent deterministic approximation counting algorithms for these two models. Our method also has a provably better theoretical performance compared with the transfer matrix method.